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! Approximate Ratios<nowiki>*</nowiki>
! Approximate Ratios<nowiki>*</nowiki>
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" |[[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names| SKULO notation]] (K or S = 1, U = 2)
! colspan="2" |[[Solfege|Solfeges]]
! colspan="2" | [[Solfege| Solfeges]]
|-
|-
| 0
| 0
Line 37: Line 37:
| P1
| P1
| D
| D
|Perfect unison
| Perfect unison
|P1
| P1
|D
| D
|da
| da
| do
| do
|-
|-
Line 49: Line 49:
| ^1
| ^1
| ^D
| ^D
|comma-wide unison,  
| comma-wide unison,  
super unison
super unison
|K1, S1
| K1, S1
|KD, SD
| KD, SD
|du
| du
| di
| di
|-
|-
Line 62: Line 62:
| vm2
| vm2
| vEb
| vEb
|subminor 2nd, uber unison
| subminor 2nd, uber unison
|sm2, U1
| sm2, U1
|sEb, UD
| sEb, UD
|fro
| fro
| ro
| ro
|-
|-
Line 74: Line 74:
| m2
| m2
| Eb
| Eb
|minor 2nd,  
| minor 2nd,  
classic augmented unison
classic augmented unison
|m2, kkA1
| m2, kkA1
|Eb, kkD#
| Eb, kkD#
|fra
| fra
| rih
| rih
|-
|-
Line 87: Line 87:
| ^m2
| ^m2
| ^Eb
| ^Eb
|classic minor 2nd,  
| classic minor 2nd,  
comma-narrow aug unison
comma-narrow aug unison
|Km2, kA1
| Km2, kA1
|KEb, kD#
| KEb, kD#
|fru
| fru
| ra
| ra
|-
|-
Line 100: Line 100:
| ^^m2
| ^^m2
| ^^Eb
| ^^Eb
|lesser neutral second, augmented unison
| lesser neutral second, augmented unison
|n2, A1
| n2, A1
|UEb, D#
| UEb, D#
|fri
| fri
| ru **
| ru **
|-
|-
Line 112: Line 112:
| vvM2
| vvM2
| vvE
| vvE
|greater neutral second,  
| greater neutral second,  
super aug unison
super aug unison
|N2, sA1
| N2, sA1
|uE, sD#
| uE, sD#
|ri
| ri
| ruh ***
| ruh ***
|-
|-
Line 125: Line 125:
| vM2
| vM2
| vE
| vE
|classic/comma-narrow major 2nd
| classic/comma-narrow major 2nd
|kM2
| kM2
|kE
| kE
|ro
| ro
| reh
| reh
|-
|-
Line 137: Line 137:
| M2
| M2
| E
| E
|major 2nd
| major 2nd
|M2
| M2
|E
| E
|ra
| ra
| re
| re
|-
|-
Line 149: Line 149:
| ^M2
| ^M2
| ^E
| ^E
|supermajor 2nd
| supermajor 2nd
|SM2
| SM2
|SE
| SE
|ru
| ru
| ri
| ri
|-
|-
Line 161: Line 161:
| vm3
| vm3
| vF
| vF
|subminor 3rd
| subminor 3rd
|sm3
| sm3
|sF
| sF
|no
| no
| ma
| ma
|-
|-
Line 173: Line 173:
| m3
| m3
| F
| F
|minor 3rd
| minor 3rd
|m3
| m3
|F
| F
|na
| na
| meh
| meh
|-
|-
Line 185: Line 185:
| ^m3
| ^m3
| ^F
| ^F
|classic minor 3rd
| classic minor 3rd
|Km3
| Km3
|KF
| KF
|nu
| nu
| me
| me
|-
|-
Line 197: Line 197:
| ^^m3
| ^^m3
| ^^F
| ^^F
|lesser neutral 3rd
| lesser neutral 3rd
|n3
| n3
|UF
| UF
|ni
| ni
| mu **
| mu **
|-
|-
Line 209: Line 209:
| vvM3
| vvM3
| vvF#
| vvF#
|greater neutral 3rd
| greater neutral 3rd
|N3
| N3
|uF#
| uF#
|mi
| mi
| muh ***
| muh ***
|-
|-
Line 221: Line 221:
| vM3
| vM3
| vF#
| vF#
|classic major 3rd
| classic major 3rd
|kM3
| kM3
|kF#
| kF#
|mo
| mo
| mi
| mi
|-
|-
Line 233: Line 233:
| M3
| M3
| F#
| F#
|major 3rd
| major 3rd
|M3
| M3
|F#
| F#
|ma
| ma
| maa
| maa
|-
|-
Line 245: Line 245:
| ^M3
| ^M3
| ^F#
| ^F#
|supermajor 3rd
| supermajor 3rd
|SM3
| SM3
|SF#
| SF#
|mu
| mu
| mo
| mo
|-
|-
Line 257: Line 257:
| v4
| v4
| vG
| vG
|sub 4th
| sub 4th
|s4
| s4
|sG
| sG
|fo
| fo
| fe
| fe
|-
|-
Line 269: Line 269:
| P4
| P4
| G
| G
|perfect 4th
| perfect 4th
|P4
| P4
|G
| G
|fa
| fa
| fa
| fa
|-
|-
Line 281: Line 281:
| ^4
| ^4
| ^G
| ^G
|comma-wide 4th
| comma-wide 4th
|K4
| K4
|KG
| KG
|fu
| fu
| fih
| fih
|-
|-
Line 293: Line 293:
| ^^4
| ^^4
| ^^G
| ^^G
|uber 4th, sub diminished 5th
| uber 4th, sub diminished 5th
|U4, sd5
| U4, sd5
|UG, sAb
| UG, sAb
|fi/sho
| fi/sho
| fu
| fu
|-
|-
Line 306: Line 306:
| vvA4, d5
| vvA4, d5
| vvG#, Ab
| vvG#, Ab
|classic augmented 4th, diminished 5th
| classic augmented 4th, diminished 5th
|kkA4, d5
| kkA4, d5
|kkG#, Ab
| kkG#, Ab
|pi/sha
| pi/sha
| fi
| fi
|-
|-
Line 318: Line 318:
| vA4, ^d5
| vA4, ^d5
| vG#, ^Ab
| vG#, ^Ab
|comma-narrow aug 4th,  
| comma-narrow aug 4th,  
comma-wide dim 5th
comma-wide dim 5th
|kA4, Kd5
| kA4, Kd5
|kG#, KAb
| kG#, KAb
|po/shu
| po/shu
| seh
| seh
|-
|-
Line 331: Line 331:
| A4, ^^d5
| A4, ^^d5
| G#, ^^Ab
| G#, ^^Ab
|augmented 4th,  
| augmented 4th,  
classic diminished 5th
classic diminished 5th
|A4, KKd5
| A4, KKd5
|G#, KKAb
| G#, KKAb
|pa/shi
| pa/shi
| se
| se
|-
|-
Line 344: Line 344:
| vv5
| vv5
| vvA
| vvA
|super augmented 4th,  
| super augmented 4th,  
unter 5th
unter 5th
|SA4, u5
| SA4, u5
|SG#, uA
| SG#, uA
|pu/si
| pu/si
| su
| su
|-
|-
Line 357: Line 357:
| v5
| v5
| vA
| vA
|comma-narrow 5th
| comma-narrow 5th
|k5
| k5
|kA
| kA
|so
| so
| sih
| sih
|-
|-
Line 369: Line 369:
| P5
| P5
| A
| A
|perfect 5th
| perfect 5th
|P5
| P5
|A
| A
|sa
| sa
| sol
| sol
|-
|-
Line 381: Line 381:
| ^5
| ^5
| ^A
| ^A
|super 5th
| super 5th
|S5
| S5
|SA
| SA
|su
| su
| si
| si
|-
|-
Line 393: Line 393:
| vm6
| vm6
| vBb
| vBb
|subminor 6th
| subminor 6th
|sm6
| sm6
|sBb
| sBb
|flo
| flo
| lo
| lo
|-
|-
Line 405: Line 405:
| m6
| m6
| Bb
| Bb
|minor 6th
| minor 6th
|m6
| m6
|Bb
| Bb
|fla
| fla
| leh
| leh
|-
|-
Line 417: Line 417:
| ^m6
| ^m6
| ^Bb
| ^Bb
|classic minor 6th
| classic minor 6th
|Km6
| Km6
|KBb
| KBb
|flu
| flu
| le
| le
|-
|-
Line 429: Line 429:
| ^^m6
| ^^m6
| ^^Bb
| ^^Bb
|lesser neutral 6th
| lesser neutral 6th
|n6
| n6
|UBb
| UBb
|fli
| fli
| lu **
| lu **
|-
|-
Line 441: Line 441:
| vvM6
| vvM6
| vvB
| vvB
|greater neutral 6th
| greater neutral 6th
|N6
| N6
|uB
| uB
|li
| li
| luh ***
| luh ***
|-
|-
Line 453: Line 453:
| vM6
| vM6
| vB
| vB
|classic major 6th
| classic major 6th
|kM6
| kM6
|kB
| kB
|lo
| lo
| la
| la
|-
|-
Line 465: Line 465:
| M6
| M6
| B
| B
|major 6th
| major 6th
|M6
| M6
|B
| B
|la
| la
| laa
| laa
|-
|-
Line 477: Line 477:
| ^M6
| ^M6
| ^B
| ^B
|supermajor 6th
| supermajor 6th
|SM6
| SM6
|SB
| SB
|lu
| lu
| li
| li
|-
|-
Line 489: Line 489:
| vm7
| vm7
| vC
| vC
|subminor 7th
| subminor 7th
|sm7
| sm7
|sC
| sC
|tho
| tho
| ta
| ta
|-
|-
Line 501: Line 501:
| m7
| m7
| C
| C
|minor 7th
| minor 7th
|m7
| m7
|C
| C
|tha
| tha
| teh
| teh
|-
|-
Line 513: Line 513:
| ^m7
| ^m7
| ^C
| ^C
|classic/comma-wide minor 7th
| classic/comma-wide minor 7th
|Km7
| Km7
|KC
| KC
|thu
| thu
| te
| te
|-
|-
Line 525: Line 525:
| ^^m7
| ^^m7
| ^^C
| ^^C
|lesser neutral 7th, sub diminished 8ve
| lesser neutral 7th, sub diminished 8ve
|n7, sd8
| n7, sd8
|UC, sDb
| UC, sDb
|thi
| thi
| tu **
| tu **
|-
|-
Line 537: Line 537:
| vvM7
| vvM7
| vvC#
| vvC#
|greater neutral 7th,  
| greater neutral 7th,  
diminished 8ve
diminished 8ve
|N7, d8
| N7, d8
|uC#, Db
| uC#, Db
|ti
| ti
| tuh ***
| tuh ***
|-
|-
Line 550: Line 550:
| vM7
| vM7
| vC#
| vC#
|classic major 7th,  
| classic major 7th,  
comma-wide dim 8ve
comma-wide dim 8ve
|kM7, Kd8
| kM7, Kd8
|kC#, KDb
| kC#, KDb
|to
| to
| ti
| ti
|-
|-
Line 563: Line 563:
| M7
| M7
| C#
| C#
|major 7th,  
| major 7th,  
classic diminished 8ve
classic diminished 8ve
|M7, KKd8
| M7, KKd8
|C#, KKDb
| C#, KKDb
|ta
| ta
| taa
| taa
|-
|-
Line 576: Line 576:
| ^M7
| ^M7
| ^C#
| ^C#
|supermajor 7th, unter 8ve
| supermajor 7th, unter 8ve
|SM7, u8
| SM7, u8
|SC#, uD
| SC#, uD
|tu
| tu
| to
| to
|-
|-
Line 588: Line 588:
| v8
| v8
| vD
| vD
|comma-narrow 8ve, sub 8ve
| comma-narrow 8ve, sub 8ve
|k8/s8
| k8/s8
|kD, sD
| kD, sD
|do
| do
| da
| da
|-
|-
Line 600: Line 600:
| P8
| P8
| D
| D
|perfect 8ve
| perfect 8ve
|P8
| P8
|D
| D
|da
| da
| do
| do
|}
|}
Line 746: Line 746:
== Approximation to JI ==
== Approximation to JI ==
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]
[[File:46ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 15-limit intervals approximated in 46edo]]
=== 15-odd-limit interval mappings ===
=== Interval mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
{{Q-odd-limit intervals|46}}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+style=white-space:nowrap| 15-odd-limit intervals by direct mapping (even if inconsistent)
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
! Error (rel, [[Relative cent|%]])
|-
| [[11/7]], [[14/11]]
| 0.117
| 0.4
|-
| [[9/5]], [[10/9]]
| 0.205
| 0.8
|-
| [[13/7]], [[14/13]]
| 2.137
| 8.2
|-
| [[13/11]], [[22/13]]
| 2.253
| 8.6
|-
| '''[[3/2]], [[4/3]]'''
| '''2.393'''
| '''9.2'''
|-
| [[5/3]], [[6/5]]
| 2.598
| 10.0
|-
| '''[[11/8]], [[16/11]]'''
| '''3.492'''
| '''13.4'''
|-
| '''[[7/4]], [[8/7]]'''
| '''3.609'''
| '''13.8'''
|-
| [[9/8]], [[16/9]]
| 4.786
| 18.3
|-
| '''[[5/4]], [[8/5]]'''
| '''4.991'''
| '''19.1'''
|-
| '''[[13/8]], [[16/13]]'''
| '''5.745'''
| '''22.0'''
|-
| [[11/6]], [[12/11]]
| 5.885
| 22.6
|-
| [[7/6]], [[12/7]]
| 6.001
| 23.0
|-
| [[15/8]], [[16/15]]
| 7.383
| 28.3
|-
| [[13/12]], [[24/13]]
| 8.138
| 31.2
|-
| [[11/9]], [[18/11]]
| 8.278
| 31.7
|-
| [[9/7]], [[14/9]]
| 8.394
| 32.2
|-
| [[11/10]], [[20/11]]
| 8.482
| 32.5
|-
| [[7/5]], [[10/7]]
| 8.599
| 33.0
|-
| [[18/13]], [[13/9]]
| 10.531
| 40.4
|-
| [[13/10]], [[20/13]]
| 10.736
| 41.2
|-
| [[15/11]], [[22/15]]
| 10.875
| 41.7
|-
| [[15/14]], [[28/15]]
| 10.992
| 42.1
|-
| ''[[15/13]], [[26/15]]''
| ''12.958''
| ''49.7''
|}
{{15-odd-limit|46}}


== Regular temperament properties ==
== Regular temperament properties ==
Retrieved from "https://en.xen.wiki/w/46edo"